The Core of a Partition Function Game

In a partition function game the worth of a deviation depends on the reaction of outsiders; the beliefs about the possible reaction are crucial for the stability of an existing agreement. In contrast with existing approaches we look at the residual reaction from the point of view of the residual players. In our assumption the residual players engage in a similar game, and if they find equilibrium outcomes –in the same sense as equilibrium outcomes are defined for the main game– we can discard other outcomes as unrealistic. This gives a recursive definition of the core for partition function games. Our main result proves that this concept reduces sensitivity to behavioural assumption